// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_HOMOGENEOUS_H
#define EIGEN_HOMOGENEOUS_H

namespace Eigen {

/** \geometry_module \ingroup Geometry_Module
 *
 * \class Homogeneous
 *
 * \brief Expression of one (or a set of) homogeneous vector(s)
 *
 * \param MatrixType the type of the object in which we are making homogeneous
 *
 * This class represents an expression of one (or a set of) homogeneous vector(s).
 * It is the return type of MatrixBase::homogeneous() and most of the time
 * this is the only way it is used.
 *
 * \sa MatrixBase::homogeneous()
 */

namespace internal {

template<typename MatrixType, int Direction>
struct traits<Homogeneous<MatrixType, Direction>> : traits<MatrixType>
{
	typedef typename traits<MatrixType>::StorageKind StorageKind;
	typedef typename ref_selector<MatrixType>::type MatrixTypeNested;
	typedef typename remove_reference<MatrixTypeNested>::type _MatrixTypeNested;
	enum
	{
		RowsPlusOne = (MatrixType::RowsAtCompileTime != Dynamic) ? int(MatrixType::RowsAtCompileTime) + 1 : Dynamic,
		ColsPlusOne = (MatrixType::ColsAtCompileTime != Dynamic) ? int(MatrixType::ColsAtCompileTime) + 1 : Dynamic,
		RowsAtCompileTime = Direction == Vertical ? RowsPlusOne : MatrixType::RowsAtCompileTime,
		ColsAtCompileTime = Direction == Horizontal ? ColsPlusOne : MatrixType::ColsAtCompileTime,
		MaxRowsAtCompileTime = RowsAtCompileTime,
		MaxColsAtCompileTime = ColsAtCompileTime,
		TmpFlags = _MatrixTypeNested::Flags & HereditaryBits,
		Flags = ColsAtCompileTime == 1	 ? (TmpFlags & ~RowMajorBit)
				: RowsAtCompileTime == 1 ? (TmpFlags | RowMajorBit)
										 : TmpFlags
	};
};

template<typename MatrixType, typename Lhs>
struct homogeneous_left_product_impl;
template<typename MatrixType, typename Rhs>
struct homogeneous_right_product_impl;

} // end namespace internal

template<typename MatrixType, int _Direction>
class Homogeneous
	: public MatrixBase<Homogeneous<MatrixType, _Direction>>
	, internal::no_assignment_operator
{
  public:
	typedef MatrixType NestedExpression;
	enum
	{
		Direction = _Direction
	};

	typedef MatrixBase<Homogeneous> Base;
	EIGEN_DENSE_PUBLIC_INTERFACE(Homogeneous)

	EIGEN_DEVICE_FUNC explicit inline Homogeneous(const MatrixType& matrix)
		: m_matrix(matrix)
	{
	}

	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index rows() const EIGEN_NOEXCEPT
	{
		return m_matrix.rows() + (int(Direction) == Vertical ? 1 : 0);
	}
	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index cols() const EIGEN_NOEXCEPT
	{
		return m_matrix.cols() + (int(Direction) == Horizontal ? 1 : 0);
	}

	EIGEN_DEVICE_FUNC const NestedExpression& nestedExpression() const { return m_matrix; }

	template<typename Rhs>
	EIGEN_DEVICE_FUNC inline const Product<Homogeneous, Rhs> operator*(const MatrixBase<Rhs>& rhs) const
	{
		eigen_assert(int(Direction) == Horizontal);
		return Product<Homogeneous, Rhs>(*this, rhs.derived());
	}

	template<typename Lhs>
	friend EIGEN_DEVICE_FUNC inline const Product<Lhs, Homogeneous> operator*(const MatrixBase<Lhs>& lhs,
																			  const Homogeneous& rhs)
	{
		eigen_assert(int(Direction) == Vertical);
		return Product<Lhs, Homogeneous>(lhs.derived(), rhs);
	}

	template<typename Scalar, int Dim, int Mode, int Options>
	friend EIGEN_DEVICE_FUNC inline const Product<Transform<Scalar, Dim, Mode, Options>, Homogeneous> operator*(
		const Transform<Scalar, Dim, Mode, Options>& lhs,
		const Homogeneous& rhs)
	{
		eigen_assert(int(Direction) == Vertical);
		return Product<Transform<Scalar, Dim, Mode, Options>, Homogeneous>(lhs, rhs);
	}

	template<typename Func>
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::result_of<Func(Scalar, Scalar)>::type redux(
		const Func& func) const
	{
		return func(m_matrix.redux(func), Scalar(1));
	}

  protected:
	typename MatrixType::Nested m_matrix;
};

/** \geometry_module \ingroup Geometry_Module
 *
 * \returns a vector expression that is one longer than the vector argument, with the value 1 symbolically appended as
 * the last coefficient.
 *
 * This can be used to convert affine coordinates to homogeneous coordinates.
 *
 * \only_for_vectors
 *
 * Example: \include MatrixBase_homogeneous.cpp
 * Output: \verbinclude MatrixBase_homogeneous.out
 *
 * \sa VectorwiseOp::homogeneous(), class Homogeneous
 */
template<typename Derived>
EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::HomogeneousReturnType
MatrixBase<Derived>::homogeneous() const
{
	EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
	return HomogeneousReturnType(derived());
}

/** \geometry_module \ingroup Geometry_Module
 *
 * \returns an expression where the value 1 is symbolically appended as the final coefficient to each column (or row) of
 * the matrix.
 *
 * This can be used to convert affine coordinates to homogeneous coordinates.
 *
 * Example: \include VectorwiseOp_homogeneous.cpp
 * Output: \verbinclude VectorwiseOp_homogeneous.out
 *
 * \sa MatrixBase::homogeneous(), class Homogeneous */
template<typename ExpressionType, int Direction>
EIGEN_DEVICE_FUNC inline Homogeneous<ExpressionType, Direction>
VectorwiseOp<ExpressionType, Direction>::homogeneous() const
{
	return HomogeneousReturnType(_expression());
}

/** \geometry_module \ingroup Geometry_Module
  *
  * \brief homogeneous normalization
  *
  * \returns a vector expression of the N-1 first coefficients of \c *this divided by that last coefficient.
  *
  * This can be used to convert homogeneous coordinates to affine coordinates.
  *
  * It is essentially a shortcut for:
  * \code
	this->head(this->size()-1)/this->coeff(this->size()-1);
	\endcode
  *
  * Example: \include MatrixBase_hnormalized.cpp
  * Output: \verbinclude MatrixBase_hnormalized.out
  *
  * \sa VectorwiseOp::hnormalized() */
template<typename Derived>
EIGEN_DEVICE_FUNC inline const typename MatrixBase<Derived>::HNormalizedReturnType
MatrixBase<Derived>::hnormalized() const
{
	EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
	return ConstStartMinusOne(
			   derived(), 0, 0, ColsAtCompileTime == 1 ? size() - 1 : 1, ColsAtCompileTime == 1 ? 1 : size() - 1) /
		   coeff(size() - 1);
}

/** \geometry_module \ingroup Geometry_Module
 *
 * \brief column or row-wise homogeneous normalization
 *
 * \returns an expression of the first N-1 coefficients of each column (or row) of \c *this divided by the last
 * coefficient of each column (or row).
 *
 * This can be used to convert homogeneous coordinates to affine coordinates.
 *
 * It is conceptually equivalent to calling MatrixBase::hnormalized() to each column (or row) of \c *this.
 *
 * Example: \include DirectionWise_hnormalized.cpp
 * Output: \verbinclude DirectionWise_hnormalized.out
 *
 * \sa MatrixBase::hnormalized() */
template<typename ExpressionType, int Direction>
EIGEN_DEVICE_FUNC inline const typename VectorwiseOp<ExpressionType, Direction>::HNormalizedReturnType
VectorwiseOp<ExpressionType, Direction>::hnormalized() const
{
	return HNormalized_Block(_expression(),
							 0,
							 0,
							 Direction == Vertical ? _expression().rows() - 1 : _expression().rows(),
							 Direction == Horizontal ? _expression().cols() - 1 : _expression().cols())
		.cwiseQuotient(Replicate < HNormalized_Factors,
					   Direction == Vertical ? HNormalized_SizeMinusOne : 1,
					   Direction == Horizontal
						   ? HNormalized_SizeMinusOne
						   : 1 > (HNormalized_Factors(_expression(),
													  Direction == Vertical ? _expression().rows() - 1 : 0,
													  Direction == Horizontal ? _expression().cols() - 1 : 0,
													  Direction == Vertical ? 1 : _expression().rows(),
													  Direction == Horizontal ? 1 : _expression().cols()),
								  Direction == Vertical ? _expression().rows() - 1 : 1,
								  Direction == Horizontal ? _expression().cols() - 1 : 1));
}

namespace internal {

template<typename MatrixOrTransformType>
struct take_matrix_for_product
{
	typedef MatrixOrTransformType type;
	EIGEN_DEVICE_FUNC static const type& run(const type& x) { return x; }
};

template<typename Scalar, int Dim, int Mode, int Options>
struct take_matrix_for_product<Transform<Scalar, Dim, Mode, Options>>
{
	typedef Transform<Scalar, Dim, Mode, Options> TransformType;
	typedef typename internal::add_const<typename TransformType::ConstAffinePart>::type type;
	EIGEN_DEVICE_FUNC static type run(const TransformType& x) { return x.affine(); }
};

template<typename Scalar, int Dim, int Options>
struct take_matrix_for_product<Transform<Scalar, Dim, Projective, Options>>
{
	typedef Transform<Scalar, Dim, Projective, Options> TransformType;
	typedef typename TransformType::MatrixType type;
	EIGEN_DEVICE_FUNC static const type& run(const TransformType& x) { return x.matrix(); }
};

template<typename MatrixType, typename Lhs>
struct traits<homogeneous_left_product_impl<Homogeneous<MatrixType, Vertical>, Lhs>>
{
	typedef typename take_matrix_for_product<Lhs>::type LhsMatrixType;
	typedef typename remove_all<MatrixType>::type MatrixTypeCleaned;
	typedef typename remove_all<LhsMatrixType>::type LhsMatrixTypeCleaned;
	typedef typename make_proper_matrix_type<typename traits<MatrixTypeCleaned>::Scalar,
											 LhsMatrixTypeCleaned::RowsAtCompileTime,
											 MatrixTypeCleaned::ColsAtCompileTime,
											 MatrixTypeCleaned::PlainObject::Options,
											 LhsMatrixTypeCleaned::MaxRowsAtCompileTime,
											 MatrixTypeCleaned::MaxColsAtCompileTime>::type ReturnType;
};

template<typename MatrixType, typename Lhs>
struct homogeneous_left_product_impl<Homogeneous<MatrixType, Vertical>, Lhs>
	: public ReturnByValue<homogeneous_left_product_impl<Homogeneous<MatrixType, Vertical>, Lhs>>
{
	typedef typename traits<homogeneous_left_product_impl>::LhsMatrixType LhsMatrixType;
	typedef typename remove_all<LhsMatrixType>::type LhsMatrixTypeCleaned;
	typedef typename remove_all<typename LhsMatrixTypeCleaned::Nested>::type LhsMatrixTypeNested;
	EIGEN_DEVICE_FUNC homogeneous_left_product_impl(const Lhs& lhs, const MatrixType& rhs)
		: m_lhs(take_matrix_for_product<Lhs>::run(lhs))
		, m_rhs(rhs)
	{
	}

	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index rows() const EIGEN_NOEXCEPT { return m_lhs.rows(); }
	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index cols() const EIGEN_NOEXCEPT { return m_rhs.cols(); }

	template<typename Dest>
	EIGEN_DEVICE_FUNC void evalTo(Dest& dst) const
	{
		// FIXME investigate how to allow lazy evaluation of this product when possible
		dst = Block < const LhsMatrixTypeNested, LhsMatrixTypeNested::RowsAtCompileTime,
		LhsMatrixTypeNested::ColsAtCompileTime == Dynamic
			? Dynamic
			: LhsMatrixTypeNested::ColsAtCompileTime - 1 > (m_lhs, 0, 0, m_lhs.rows(), m_lhs.cols() - 1) * m_rhs;
		dst += m_lhs.col(m_lhs.cols() - 1).rowwise().template replicate<MatrixType::ColsAtCompileTime>(m_rhs.cols());
	}

	typename LhsMatrixTypeCleaned::Nested m_lhs;
	typename MatrixType::Nested m_rhs;
};

template<typename MatrixType, typename Rhs>
struct traits<homogeneous_right_product_impl<Homogeneous<MatrixType, Horizontal>, Rhs>>
{
	typedef typename make_proper_matrix_type<typename traits<MatrixType>::Scalar,
											 MatrixType::RowsAtCompileTime,
											 Rhs::ColsAtCompileTime,
											 MatrixType::PlainObject::Options,
											 MatrixType::MaxRowsAtCompileTime,
											 Rhs::MaxColsAtCompileTime>::type ReturnType;
};

template<typename MatrixType, typename Rhs>
struct homogeneous_right_product_impl<Homogeneous<MatrixType, Horizontal>, Rhs>
	: public ReturnByValue<homogeneous_right_product_impl<Homogeneous<MatrixType, Horizontal>, Rhs>>
{
	typedef typename remove_all<typename Rhs::Nested>::type RhsNested;
	EIGEN_DEVICE_FUNC homogeneous_right_product_impl(const MatrixType& lhs, const Rhs& rhs)
		: m_lhs(lhs)
		, m_rhs(rhs)
	{
	}

	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index rows() const EIGEN_NOEXCEPT { return m_lhs.rows(); }
	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index cols() const EIGEN_NOEXCEPT { return m_rhs.cols(); }

	template<typename Dest>
	EIGEN_DEVICE_FUNC void evalTo(Dest& dst) const
	{
		// FIXME investigate how to allow lazy evaluation of this product when possible
		dst = m_lhs * Block < const RhsNested,
		RhsNested::RowsAtCompileTime == Dynamic ? Dynamic : RhsNested::RowsAtCompileTime - 1,
		RhsNested::ColsAtCompileTime > (m_rhs, 0, 0, m_rhs.rows() - 1, m_rhs.cols());
		dst += m_rhs.row(m_rhs.rows() - 1).colwise().template replicate<MatrixType::RowsAtCompileTime>(m_lhs.rows());
	}

	typename MatrixType::Nested m_lhs;
	typename Rhs::Nested m_rhs;
};

template<typename ArgType, int Direction>
struct evaluator_traits<Homogeneous<ArgType, Direction>>
{
	typedef typename storage_kind_to_evaluator_kind<typename ArgType::StorageKind>::Kind Kind;
	typedef HomogeneousShape Shape;
};

template<>
struct AssignmentKind<DenseShape, HomogeneousShape>
{
	typedef Dense2Dense Kind;
};

template<typename ArgType, int Direction>
struct unary_evaluator<Homogeneous<ArgType, Direction>, IndexBased>
	: evaluator<typename Homogeneous<ArgType, Direction>::PlainObject>
{
	typedef Homogeneous<ArgType, Direction> XprType;
	typedef typename XprType::PlainObject PlainObject;
	typedef evaluator<PlainObject> Base;

	EIGEN_DEVICE_FUNC explicit unary_evaluator(const XprType& op)
		: Base()
		, m_temp(op)
	{
		::new (static_cast<Base*>(this)) Base(m_temp);
	}

  protected:
	PlainObject m_temp;
};

// dense = homogeneous
template<typename DstXprType, typename ArgType, typename Scalar>
struct Assignment<DstXprType,
				  Homogeneous<ArgType, Vertical>,
				  internal::assign_op<Scalar, typename ArgType::Scalar>,
				  Dense2Dense>
{
	typedef Homogeneous<ArgType, Vertical> SrcXprType;
	EIGEN_DEVICE_FUNC static void run(DstXprType& dst,
									  const SrcXprType& src,
									  const internal::assign_op<Scalar, typename ArgType::Scalar>&)
	{
		Index dstRows = src.rows();
		Index dstCols = src.cols();
		if ((dst.rows() != dstRows) || (dst.cols() != dstCols))
			dst.resize(dstRows, dstCols);

		dst.template topRows<ArgType::RowsAtCompileTime>(src.nestedExpression().rows()) = src.nestedExpression();
		dst.row(dst.rows() - 1).setOnes();
	}
};

// dense = homogeneous
template<typename DstXprType, typename ArgType, typename Scalar>
struct Assignment<DstXprType,
				  Homogeneous<ArgType, Horizontal>,
				  internal::assign_op<Scalar, typename ArgType::Scalar>,
				  Dense2Dense>
{
	typedef Homogeneous<ArgType, Horizontal> SrcXprType;
	EIGEN_DEVICE_FUNC static void run(DstXprType& dst,
									  const SrcXprType& src,
									  const internal::assign_op<Scalar, typename ArgType::Scalar>&)
	{
		Index dstRows = src.rows();
		Index dstCols = src.cols();
		if ((dst.rows() != dstRows) || (dst.cols() != dstCols))
			dst.resize(dstRows, dstCols);

		dst.template leftCols<ArgType::ColsAtCompileTime>(src.nestedExpression().cols()) = src.nestedExpression();
		dst.col(dst.cols() - 1).setOnes();
	}
};

template<typename LhsArg, typename Rhs, int ProductTag>
struct generic_product_impl<Homogeneous<LhsArg, Horizontal>, Rhs, HomogeneousShape, DenseShape, ProductTag>
{
	template<typename Dest>
	EIGEN_DEVICE_FUNC static void evalTo(Dest& dst, const Homogeneous<LhsArg, Horizontal>& lhs, const Rhs& rhs)
	{
		homogeneous_right_product_impl<Homogeneous<LhsArg, Horizontal>, Rhs>(lhs.nestedExpression(), rhs).evalTo(dst);
	}
};

template<typename Lhs, typename Rhs>
struct homogeneous_right_product_refactoring_helper
{
	enum
	{
		Dim = Lhs::ColsAtCompileTime,
		Rows = Lhs::RowsAtCompileTime
	};
	typedef typename Rhs::template ConstNRowsBlockXpr<Dim>::Type LinearBlockConst;
	typedef typename remove_const<LinearBlockConst>::type LinearBlock;
	typedef typename Rhs::ConstRowXpr ConstantColumn;
	typedef Replicate<const ConstantColumn, Rows, 1> ConstantBlock;
	typedef Product<Lhs, LinearBlock, LazyProduct> LinearProduct;
	typedef CwiseBinaryOp<internal::scalar_sum_op<typename Lhs::Scalar, typename Rhs::Scalar>,
						  const LinearProduct,
						  const ConstantBlock>
		Xpr;
};

template<typename Lhs, typename Rhs, int ProductTag>
struct product_evaluator<Product<Lhs, Rhs, LazyProduct>, ProductTag, HomogeneousShape, DenseShape>
	: public evaluator<typename homogeneous_right_product_refactoring_helper<typename Lhs::NestedExpression, Rhs>::Xpr>
{
	typedef Product<Lhs, Rhs, LazyProduct> XprType;
	typedef homogeneous_right_product_refactoring_helper<typename Lhs::NestedExpression, Rhs> helper;
	typedef typename helper::ConstantBlock ConstantBlock;
	typedef typename helper::Xpr RefactoredXpr;
	typedef evaluator<RefactoredXpr> Base;

	EIGEN_DEVICE_FUNC explicit product_evaluator(const XprType& xpr)
		: Base(xpr.lhs().nestedExpression().lazyProduct(
				   xpr.rhs().template topRows<helper::Dim>(xpr.lhs().nestedExpression().cols())) +
			   ConstantBlock(xpr.rhs().row(xpr.rhs().rows() - 1), xpr.lhs().rows(), 1))
	{
	}
};

template<typename Lhs, typename RhsArg, int ProductTag>
struct generic_product_impl<Lhs, Homogeneous<RhsArg, Vertical>, DenseShape, HomogeneousShape, ProductTag>
{
	template<typename Dest>
	EIGEN_DEVICE_FUNC static void evalTo(Dest& dst, const Lhs& lhs, const Homogeneous<RhsArg, Vertical>& rhs)
	{
		homogeneous_left_product_impl<Homogeneous<RhsArg, Vertical>, Lhs>(lhs, rhs.nestedExpression()).evalTo(dst);
	}
};

// TODO: the following specialization is to address a regression from 3.2 to 3.3
// In the future, this path should be optimized.
template<typename Lhs, typename RhsArg, int ProductTag>
struct generic_product_impl<Lhs, Homogeneous<RhsArg, Vertical>, TriangularShape, HomogeneousShape, ProductTag>
{
	template<typename Dest>
	static void evalTo(Dest& dst, const Lhs& lhs, const Homogeneous<RhsArg, Vertical>& rhs)
	{
		dst.noalias() = lhs * rhs.eval();
	}
};

template<typename Lhs, typename Rhs>
struct homogeneous_left_product_refactoring_helper
{
	enum
	{
		Dim = Rhs::RowsAtCompileTime,
		Cols = Rhs::ColsAtCompileTime
	};
	typedef typename Lhs::template ConstNColsBlockXpr<Dim>::Type LinearBlockConst;
	typedef typename remove_const<LinearBlockConst>::type LinearBlock;
	typedef typename Lhs::ConstColXpr ConstantColumn;
	typedef Replicate<const ConstantColumn, 1, Cols> ConstantBlock;
	typedef Product<LinearBlock, Rhs, LazyProduct> LinearProduct;
	typedef CwiseBinaryOp<internal::scalar_sum_op<typename Lhs::Scalar, typename Rhs::Scalar>,
						  const LinearProduct,
						  const ConstantBlock>
		Xpr;
};

template<typename Lhs, typename Rhs, int ProductTag>
struct product_evaluator<Product<Lhs, Rhs, LazyProduct>, ProductTag, DenseShape, HomogeneousShape>
	: public evaluator<typename homogeneous_left_product_refactoring_helper<Lhs, typename Rhs::NestedExpression>::Xpr>
{
	typedef Product<Lhs, Rhs, LazyProduct> XprType;
	typedef homogeneous_left_product_refactoring_helper<Lhs, typename Rhs::NestedExpression> helper;
	typedef typename helper::ConstantBlock ConstantBlock;
	typedef typename helper::Xpr RefactoredXpr;
	typedef evaluator<RefactoredXpr> Base;

	EIGEN_DEVICE_FUNC explicit product_evaluator(const XprType& xpr)
		: Base(xpr.lhs()
				   .template leftCols<helper::Dim>(xpr.rhs().nestedExpression().rows())
				   .lazyProduct(xpr.rhs().nestedExpression()) +
			   ConstantBlock(xpr.lhs().col(xpr.lhs().cols() - 1), 1, xpr.rhs().cols()))
	{
	}
};

template<typename Scalar, int Dim, int Mode, int Options, typename RhsArg, int ProductTag>
struct generic_product_impl<Transform<Scalar, Dim, Mode, Options>,
							Homogeneous<RhsArg, Vertical>,
							DenseShape,
							HomogeneousShape,
							ProductTag>
{
	typedef Transform<Scalar, Dim, Mode, Options> TransformType;
	template<typename Dest>
	EIGEN_DEVICE_FUNC static void evalTo(Dest& dst, const TransformType& lhs, const Homogeneous<RhsArg, Vertical>& rhs)
	{
		homogeneous_left_product_impl<Homogeneous<RhsArg, Vertical>, TransformType>(lhs, rhs.nestedExpression())
			.evalTo(dst);
	}
};

template<typename ExpressionType, int Side, bool Transposed>
struct permutation_matrix_product<ExpressionType, Side, Transposed, HomogeneousShape>
	: public permutation_matrix_product<ExpressionType, Side, Transposed, DenseShape>
{};

} // end namespace internal

} // end namespace Eigen

#endif // EIGEN_HOMOGENEOUS_H
